How do you solve a/15=4/5?

4 Answers
Mar 27, 2018

color(teal)(a=12

Explanation:

Simply use cross multiplication ...
color(teal)(a/15=4/5

or, color(teal)(5a=4*15

or, color(teal)(a=(4*15)/5=4*3=12

hope that helped.

Mar 27, 2018

a = 12

Explanation:

Here, a/15 = 4/5
Or,5*a = 15*4
Or,5a = 60
Or,a = 60/5
Or,a = 12

Mar 27, 2018

a=12

Explanation:

"Alternatively multiply both sides of the equation by"
"the "color(blue)"lowest common multiple of 15 and 5"

"the lowest common multiple of 15 and 5 is 15"

cancel(15)^1xxa/cancel(15)^1=cancel(15)^3xx4/cancel(5)^1

rArra=3xx4=12

Mar 27, 2018

a=12

Explanation:

color(blue)("Important fact")

A fraction's structure is such that we have:

("numerators")/("denominators") color(white)("d")->color(white)("dd") ("count")/("size indicator of what is being counted")

You can not color(purple)(ul("DIRECTLY")) add, subtract or compare the 'counts' unless the 'size indicators' are the same.

Multiply by 1 and you do not change the value of something. However, 1 comes in many forms so you change the way something looks without changing its value.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Answering the question")

color(green)(a/15=[4/5color(red)(xx1)] color(white)("dddd")->color(white)("dddd")a/15=[4/5color(red)(xx3/3) ])

color(green)(color(white)("dddddddddddddddd")->color(white)("dddd")a/15=12/15)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now that the bottom numbers or size indicators (denominators) are the same we can just compare the top numbers or counts (numerators).

Mathematically you say: multiply both sides by 15#

So we now have: a=12
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Check")

If we divide the left hand side by the right hand side we will get 1 if they are the same.

12/15-:4/5

12/15xx5/4

5/15xx12/4

1/3xx3/1=1